In a calibration of printed colors in an inkjet printer, for example, a scanner is used to measure an array of a great number of color samples (several hundred color samples) having different color tones and densities (color patch) printed on a sheet according to prescribed input information. Then the spectral reflection characteristics of the visible spectrum (400-700 nm) are measured and calibration is made to eliminate a difference between these measured reflection characteristics and the ideal reference values. To measure the aforementioned spectral reflection characteristics, an illumination receiving system of so-called 45-degrees: 0-degree geometry is used, wherein a sample surface is illuminated at an angle of incidence of 45 degrees with respect to the normal, and the light reflected from the sample surface is received at an angle of reflection of 0 degree relative to the normal. In case of a reflection characteristics measuring apparatus designed for spot measurement, it takes too much time to measure such an array composed of a great number of color samples. To solve this problem, about 20 through 40 color samples arranged in a one-dimensional array are normally measured by manual or automated scanning. Such a reflection characteristics measurement is disclosed, for example, in the Japanese Unexamined Patent Application Publication No. 2008-298579 by the inventor of the present invention.
In such measurement, however, illuminance on a sample surface by the illumination light changes according to a fluctuation in a distance between a measuring instrument and the sample surface resulting from scanning operation. Such change in illuminance results in measurement errors. To minimize the change in illuminance caused by the fluctuation in the distance, an illumination system characterized by reduced change in illuminance caused by the fluctuation in the distance is disclosed and proposed in U.S. Pat. Nos. 7,365,843 and 7,433,041. Such conventional art uses a light source known by the name of cosine emitter or Lambertian emitter. To be more specific, as shown in FIG. 14, the light source S has a spatial distribution of Lambertian characteristics (cosine characteristics), that is, the light source S is a diffusing plane light source. This light source S is arranged in such a way that the center axis X of the spatial distribution will be parallel with the normal N of the sample surface, namely, the light source S and the sample surface will be arranged in parallel with each other, and the distance D1 between the normal N and the center axis X will be equal to the distance D2 between the light source S and the surface including the sample surface. This arrangement ensures that the sample surface is illuminated by the component of light flux from the light source S at an angle of incidence of “a”=45 degrees with respect to the normal N of the sample surface, whereby the aforementioned 45-degrees: 0-degree geometry is implemented.
The following describes the change in illuminance on the sample surface when the distance between the light source S and the surface including the sample surface has changed from D2 to D2+d, the distance L between the light source S and the center O of the measured area on the sample surface has changed to L′, and the angle a has changed to a′. The distance L between the light source S and the center O of the measured area equals to D1/sin (a), and the density of the light flux is inversely proportional to the square of the distance L. Thus the density of the light flux is proportional to sin2 (a). In the meantime, the density of the light flux emitted at an outgoing angle of “a” from the light source S of Lambertian characteristics is proportional to cos (a), and the density of the light flux entering the sample surface at an angle of incidence of “a” is also proportional to cos (a). Thus, the density of the light flux entering the center “O” from the light source S of Lamberitan characteristics is proportional to sin2 (a)·cos2 (a), and hence is proportional to sin2 (2·a). Since the sin2 (2·a) is maximized at “a”=45 degrees where the differential coefficient is 0, the change ratio in illuminance on the sample surface caused by the change in “a” is minimized when “a” is in the vicinity of 45 degrees. This means that the change ratio in illuminance on the sample surface caused by the change in the distance D2 between the light source S and the surface including the sample surface is minimized when “a” is in the vicinity 45 degrees. FIG. 15 is a chart representing a change in illuminance on the sample surface caused by the fluctuation in the distance between the light source S and the surface including the sample surface in the geometry of FIG. 14. The chart shows a change in illuminance caused by a fluctuation in the distance between the light source S and the surface including the sample surface, when the light source S has the spatial distribution of Lambertian characteristics (⋄), and when it has a uniform spatial distribution in the vicinity of 45 degrees independently of angle “a” (□). The “x” axis represents a change ratio in the distance, and the “y” axis indicates a change ratio in illuminance As will be apparent from FIG. 15, in the case of a light source of Lambertian characteristics, a change in illuminance is substantially reduced. For example, when the fluctuation in the distance is 2% (0.16 mm) at D2=D1=8 mm, the illuminance changes 1, and an error of about 1% occurs in the reflection characteristics measurements in case of a light source without Lambertian characteristics. In the case of a light source with Lambertian characteristics, on the other hand, the error is only 0.04%.
As described above, the technique disclosed in U.S. Pat. Nos. 7,365,843 and 7,433,041 substantially reduces a change in illuminance caused by the fluctuation in a distance between the light source S and the surface including the sample surface, namely, a distance between the illumination apparatus and the sample surface. However, the illumination efficiency is extremely poor, because the sample is illuminated by only the component in the vicinity of one direction of 45 degrees relative to the center axis of the spatial distribution of Lambertian characteristics (cosine characteristics) emitted into the hemisphere by the light source S such as an LED.